The Effect of Spatial Autocorrelation on the Error Rates of the Linear Discriminant Functions

Abstract

The problem of classification of the realization of the intrinsically stationary multivariate Gaussian random field into one of two populations with different means and factorized covariance matrices is considered. Unknown means and the common covariance matrix of the feature vector components are estimated from the spatially correlated training samples assuming spatial correlations to be known. Two plug‐in linear discriminant functions (DF) are considered. The first linear DF uses the maximum likelihood (ML) estimators of means and the bias‐adjusted ML estimator of covariance. The second one uses usual sample means and bias‐adjusted sample covariance. The first‐order asymptotic expansions with respect to the inverses of training sample sizes of the expected error rate associated with two plug‐in DF's are presented. The numerical results obtained allow us to compare the performance of the suggested DF's. The numerical calculations are done for the exponential spatial correlation function.